Advanced Chemistry Topics
Femtochemistry JCE
Mark David Ellison, Wittenberg University
Students explore a simple solution to the time-dependent Schrödinger equation in the context of understanding femtochemistryl. After a review of the time-independent harmonic oscillator model studentsstudy the process of exciting molecules with an ultrafast laser pulse and in a superposition that has time-dependent behavior.
Finding Molecular Vibrational Frequencies from HCl to SO2 JCE
Franklin M.C. Chen, University of Wisconsin-Green Bay
Theresa Julia Zielinski, Monmouth University
Students learn about finding molecular vibrational frequencies through normal mode analysis and numerical solutions for simple molecule such as HCl and more complicate molecules such as CO2 and SO2. Topics such as displacement coordinates, internal coordinates, symmetry coordinates, and their relationship are developed.
Introduction to the Basic Terms of Band Structures JCE
Gion Calzaferri, University of Berne
Stephan Glaus, University of Berne
Marc Meyer, University of Berne
In this Mathcad document you will find an explanation of the concepts and applications of band structures, translational symmetry, crystal orbitals, Bloch functions, wave vectors, the Peierls distortion, density of states (DOS), crystal orbital overlap population (COOP), and Brillouin zones.
Learning Molecular Geometry & Symmetry Through Quantum Computations and Mathcad™ Exercises JCE
Franklin M.C. Chen, University of Wisconsin-Green Bay
A Mathcad template to help students learn about molecular geometry and symmetry calculations based on the coordinate datagenerated from quantum computation software such as HyperChem. The molecular coordinate data serve as excellent real-world materials for students to appreciate the applications of linear algebra and to refresh their algebra learning experiences about linear transformations learn about fundamental properties of quantum and symmetry operators.
Maple-Assisted Template for Automatic Calculation of Second Order AA'BB' NMR Spectra JCE
Mihai Scarlete, Bishops University
This paper presents a Maple template for the interpretation and simulation of second order AA'BB' NMR-spectra, starting from the core information offered in a regular, undergraduate physical chemistry course.
Modeling pH in Natural Waters JCE
Morten Sielemann
Niels Peder Raj Andersen
Kristian Keiding
Modelling the pH variation in rivers is an interesting exercise, not only from an environmental point of view, but also because it makes use of basic physical, chemical, biological and numerical principles obtained through undergraduate courses. The pH model is built systematically using theory and logical assumptions to include or exclude different parameters and processes. After that, a short discussion will show how the initialisation values were found. The final model will show how equilibrium problems can be solved in discreet steps for a dynamic system using the simple assumption, that equilibrium reactions are much faster than transport phenomena and biological transformation. Furthermore, the model will be used to predict the behaviour of pH when changing temperature, ionic strength, buffer capacity and biological transformation rates.
The Morse Oscillator
Kevin Lehmann, Princeton University
In this worksheet, we find a presentation of the vibrational motion of a diatomic molecule held together with a potential function of a special form known as the Morse Potential. Both the classical and quantum motion of the oscillator will be studied, and explicit expressions for eigenenergies and wavefunctions are given The effect of rotation is also discusses. The document contains embedded 20 exercises and 4 advanced problems for users to test their mastery of the topic.
Using a Computer to Help Understand How Symmetry Principles Reduce Calculations JCE
Louis Kijewski, Monmouth University
This Mathcad document uses symmetry to simplify the evaluation of an eigenvalue problem by reducing a matrix to sparse form. The sparse matrix is then transformed to block diagonal form. Group theory is used to set up the calculations without going through the proofs of the methods. The ability to use symmetry principles to get the vibrational frequencies and other information about molecules with symmetry is an important asset to any chemist.
Visualization of Wavefunctions of the Ionized Hydrogen Molecule JCE
John L. Johnson, The Pennsylvania State University
Mathcad and the Shooting Method, are used to solve the Schrodinger equation for the H2+ molecule. The angular portions of the wavefunctions are the spheroidal harmonics, which when plotted show the shapes of molecular orbitals. These exact solutions are compared with those obtained from the LCAO method, using hydrogenic orbitals as basis functions. Plot of the electronic charge densities show the concentration of charge that distinguishes bonding and anti-bonding states. The energies of the wavefunctions as a function of internuclear distance for the eight lowest molecular energy states are calculated.